Dependently typed functional programming languages such as Agda are capable of expressing very precise types for data. When those data themselves encode types, we gain a powerful mechanism for abstracting generic operations over carefully circumscribed universes. This course will begin with a rapid dependently-typed programming primer in Agda, then explore techniques for and consequences of universe constructions. Of central importance are the “pattern functors” which determine the node structure of inductive and coinductive datatypes. We shall consider syntactic presentations of these functors (allowing operations as useful as symbolic differentiation), and relate them to the more uniform abstract notion of “container”. We shall expose the double-life containers lead as “interaction structures” describing systems of effects. Later, we step up to functors over universes, acquiring the power of inductive-recursive definitions, and we use that power to build universes of dependent types.

This course receives financial support from the Complex Systems Engineering theme of SICSA, the Scottish Informatics and Computer Science Alliance.

Location:
Lab sessions will take place in 4.12, Appleton Tower
Labs will start on 14 November and run every week
Lectures will take place in room 2.33, Informatics Forum
Lectures will start on 14 November and run (roughly) every 2 weeks (see schedule below)

Mailing List:
Course announcements, discussions and questions are welcome in the agda-course-13@inf.ed.ac.uk mailing list. Non-registrants: you are welcome to join too, please email Danel or Sam in the addresses above to join, with some indication you are not a machine.